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Tokyo Probability Seminar
Seminar information archive ～11/08｜Next seminar｜Future seminars 11/09～
| Date, time & place | Monday 16:00 - 17:30 122Room #122 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima (Keio Univ.), Masato Hoshino (Science Tokyo), Masahisa Ebina (Science Tokyo) |
Future seminars
2026/11/09
14:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
The classroom is 123. We are having teatime from 15:20 in the common room on the second floor. Please join us.
Ignacio Madrid (The University of Tokyo) 14:00-15:30
Explaining exclusion-like current large deviations in a single-particle diffusion-renewal system
ディリクレ空間で、準至る所ベクトル束を作り、マルコフ過程に沿って準至る所ベクトルを平行移動する。
The classroom is 123. We are having teatime from 15:20 in the common room on the second floor. Please join us.
Ignacio Madrid (The University of Tokyo) 14:00-15:30
Explaining exclusion-like current large deviations in a single-particle diffusion-renewal system
[ Abstract ]
In recent experiments, Henri Vo Van Qui and Nicolas Clément (LIMMS, CNRS - IIS UTokyo) measure with astonishing precision the electrical current (net electron counts over time) created by molecules diffusing independently between two electrodes, where they can repeatedly receive or release single electrons. There, in a diffusion-limited regime, we found that the electrical current fluctuations recover a characteristic noise reduction: the electron count has an asymptotic variance-to-mean ratio of 1/3. Surprisingly, this same factor appears in boundary-driven symmetric simple exclusion processes, where it is attributed to multi-particle spatial exclusion. In our case however, no exclusion occurs between molecules. In this talk we will elucidate mathematically the conditions allowing a single diffusing particle to achieve these same current fluctuations.
I will develop a stochastic model of a diffusing particle carrying a two-state mark (charged or uncharged). Its position is a reflected Brownian motion on an interval, while its charge state jumps through electron-transfer reactions governed by boundary local time. The scaled cumulant generating function of the electron count can then be obtained from an associated eigenproblem with Robin boundary conditions, for which we give a complementary probabilistic renewal description. The analysis provides a rigorous explanation of the observed noise reduction and makes explicit how it arises from the timing of diffusive round trips between the boundaries. Moreover, in the diffusion-limited regime, the correspondence with exclusion systems extends beyond the 1/3 factor to the full asymptotic counting statistics, after normalization by the mean current. The model thus provides a minimal single-particle instance of this general result, identifying diffusion and boundary-driven jumps as sufficient ingredients.
Kenta Misumi (The University of Tokyo) 16:00-17:30In recent experiments, Henri Vo Van Qui and Nicolas Clément (LIMMS, CNRS - IIS UTokyo) measure with astonishing precision the electrical current (net electron counts over time) created by molecules diffusing independently between two electrodes, where they can repeatedly receive or release single electrons. There, in a diffusion-limited regime, we found that the electrical current fluctuations recover a characteristic noise reduction: the electron count has an asymptotic variance-to-mean ratio of 1/3. Surprisingly, this same factor appears in boundary-driven symmetric simple exclusion processes, where it is attributed to multi-particle spatial exclusion. In our case however, no exclusion occurs between molecules. In this talk we will elucidate mathematically the conditions allowing a single diffusing particle to achieve these same current fluctuations.
I will develop a stochastic model of a diffusing particle carrying a two-state mark (charged or uncharged). Its position is a reflected Brownian motion on an interval, while its charge state jumps through electron-transfer reactions governed by boundary local time. The scaled cumulant generating function of the electron count can then be obtained from an associated eigenproblem with Robin boundary conditions, for which we give a complementary probabilistic renewal description. The analysis provides a rigorous explanation of the observed noise reduction and makes explicit how it arises from the timing of diffusive round trips between the boundaries. Moreover, in the diffusion-limited regime, the correspondence with exclusion systems extends beyond the 1/3 factor to the full asymptotic counting statistics, after normalization by the mean current. The model thus provides a minimal single-particle instance of this general result, identifying diffusion and boundary-driven jumps as sufficient ingredients.
ディリクレ空間で、準至る所ベクトル束を作り、マルコフ過程に沿って準至る所ベクトルを平行移動する。
[ Abstract ]
準正則 Dirichlet 空間上において準ベクトル束の概念を定式化することにより、その分類量として第一 Stiefel–Whitney 類が自然に現れる。さらに、この枠組みに適合する接続の理論を公理的に構築することで、対応する右過程の軌道に沿ったベクトルの準至る所での平行移動を構成することが可能となる。
この構成は、従来の Riemann 多様体あるいは sub-Riemann 多様体上の Brown 運動に沿う確率平行移動を包含するだけでなく、一般のジャンプ型過程に沿う確率平行移動も含む。さらには、RCD 空間など、特異空間上の Brown 運動に沿う確率平行移動さえも導く。
したがって本理論は、滑らかさに依存していた従来の平行移動の概念を、準正則 Dirichlet 形式と右過程を基礎とする非滑らかな対象へ拡張する一般的な枠組みを与えるものとなる。
準正則 Dirichlet 空間上において準ベクトル束の概念を定式化することにより、その分類量として第一 Stiefel–Whitney 類が自然に現れる。さらに、この枠組みに適合する接続の理論を公理的に構築することで、対応する右過程の軌道に沿ったベクトルの準至る所での平行移動を構成することが可能となる。
この構成は、従来の Riemann 多様体あるいは sub-Riemann 多様体上の Brown 運動に沿う確率平行移動を包含するだけでなく、一般のジャンプ型過程に沿う確率平行移動も含む。さらには、RCD 空間など、特異空間上の Brown 運動に沿う確率平行移動さえも導く。
したがって本理論は、滑らかさに依存していた従来の平行移動の概念を、準正則 Dirichlet 形式と右過程を基礎とする非滑らかな対象へ拡張する一般的な枠組みを与えるものとなる。
2026/11/16
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
The classroom is 002. We are having teatime from 15:20 in the common room on the second floor. Please join us.
Federica Iacovissi (Instituto Superior Técnico)
The Matrix Product Ansatz from a probabilistic viewpoint
The classroom is 002. We are having teatime from 15:20 in the common room on the second floor. Please join us.
Federica Iacovissi (Instituto Superior Técnico)
The Matrix Product Ansatz from a probabilistic viewpoint
[ Abstract ]
We provide a probabilistic characterization of the class of probability measures that can be represented by the Matrix Product Ansatz (MPA). We describe a constructive procedure, based on a suitable enlargement of the state space, showing that a probability measure can be expressed in terms of non-negative matrices via the MPA if and only if it can be written as a mixture of inhomogeneous product measures, where the mixing law is given by a Markov bridge. We illustrate this construction by applying it to examples of interacting particle systems. Finally, we discuss how the resulting probabilistic structure can be exploited to obtain large deviation principles for this class of measures. Joint work with Davide Gabrielli.
We provide a probabilistic characterization of the class of probability measures that can be represented by the Matrix Product Ansatz (MPA). We describe a constructive procedure, based on a suitable enlargement of the state space, showing that a probability measure can be expressed in terms of non-negative matrices via the MPA if and only if it can be written as a mixture of inhomogeneous product measures, where the mixing law is given by a Markov bridge. We illustrate this construction by applying it to examples of interacting particle systems. Finally, we discuss how the resulting probabilistic structure can be exploited to obtain large deviation principles for this class of measures. Joint work with Davide Gabrielli.
